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題名 作答反應與反應時間聯合模式的擴展與應用
Extensions and applications of joint modeling for responses and response times作者 蔡介文
Tsai, Jie-Wen貢獻者 余民寧
Yu, Min-Ning
蔡介文
Tsai, Jie-Wen關鍵詞 試題反應模式
反應時間模式
Gibbs抽樣
Pólya-Gamma分配
不對稱 Laplace分配
item response modeling
response time modeling
Gibbs sampler
Pólya-Gamma distribution
asymmetric Laplace distribution日期 2025 上傳時間 3-Mar-2025 14:42:24 (UTC+8) 摘要 本研究提出作答反應與反應時間聯合模式（RT-IRT 模式）的三個新擴展。這些擴展是貝氏統計中資料擴增 (DA) 策略的應用。具體來說，是利用 Pólya-Gamma (PG) 分配在 logistic 模式中實作 Gibbs 抽樣器，以及利用不對稱 Laplace 分配 (ALD) 在貝氏分量迴歸 (BQR) 中實作 Gibbs 抽樣器。 本論文包含三項主要研究。第一項研究將 PG Gibbs 抽樣器應用於 logistic RT-IRT 模式、第二項研究將 BQR 引進潛在迴歸的 RT-IRT 模式、第三項研究將 BQR 加入具有交叉關係的 RT-IRT 模式。 透過模擬研究和 TIMSS 2019 數學測驗的真實資料分析，本研究得到三個主要發現。第一，PG 方法比傳統方法（包括 MLE）表現更佳，尤其是在樣本較小（250 人）和測驗較短（15 題）的情況下。另外，在模擬條件下，BQR 在潛在迴歸模式和交叉關係模式上都表現有效。然而，對於 BQR 潛在迴歸模式，在不同分量位置上，迴歸係數並沒有明顯變化效果。相比之下，BQR 交叉關係模式在不同分量位置中顯示出明顯的交叉負荷，尤其在第 40 分量附近的模式適配效果更佳。 三種模式都具有良好的收斂特性，所有參數都在 5000 次迭代的預熱期內達到穩定。整體來說，PG Gibbs 抽樣有助於整合 logistic IRT 模式，而 BQR 方法比平均迴歸模式更加靈活且有效。此外，本研究利用 Julia 開發的統計套件支援上述擴展，讓研究人員能夠分析教育測驗中的 RT-IRT 模式。
This study proposed three new extensions of the joint modeling for responses and response times (RT-IRT models). These extensions are applications of data augmentation (DA) strategies in the Bayesian statistics. Specifically, the study utilizes the Pólya-Gamma (PG) distribution for implementing Gibbs sampler in logistic models, and the asymmetric Laplace distribution (ALD) for implementing Gibbs sampler in Bayesian quantile regressions (BQR). Three major studies were conducted. The first study applied the PG Gibbs sampler to the logistic RT-IRT models, The second study introduced the BQR to the latent regression RT-IRT models, and the third study added the BQR to the RT-IRT models with cross-relations. Through simulation studies and real data analyses using TIMSS 2019 mathematics assessment, the research revealed three key findings. One is that the PG method demonstrated better performance than traditional approaches, including MLE, particularly with smaller samples (N=250) and shorter tests (15 items). Another is that the BQR model performed effectively under simulation conditions for both latent regression and cross-relation models. However, for the BQR-based latent regression, it showed no obvious change effects of regression coefficients in different quantile levels. In contrast, the BQR-based cross-relation model shows significant cross-loadings across quantile levels, with better model fit around the 40th quantile. All three models showed good convergence properties, with parameters stabilizing within the burn-in 5000 iterations. Overall, the PG Gibbs sampling facilitates the incorporation of logistic IRT models, while BQR approaches are more flexible and effective than mean regression models. 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Past, present, and future of software for Bayesian inference. *Accepted by Statistical Science*. 描述 博士
國立政治大學
教育學系
109152512資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109152512 資料類型 thesis dc.contributor.advisor 余民寧 zh_TW dc.contributor.advisor Yu, Min-Ning en_US dc.contributor.author (Authors) 蔡介文 zh_TW dc.contributor.author (Authors) Tsai, Jie-Wen en_US dc.creator (作者) 蔡介文 zh_TW dc.creator (作者) Tsai, Jie-Wen en_US dc.date (日期) 2025 en_US dc.date.accessioned 3-Mar-2025 14:42:24 (UTC+8) - dc.date.available 3-Mar-2025 14:42:24 (UTC+8) - dc.date.issued (上傳時間) 3-Mar-2025 14:42:24 (UTC+8) - dc.identifier (Other Identifiers) G0109152512 en_US dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/156018 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 教育學系 zh_TW dc.description (描述) 109152512 zh_TW dc.description.abstract (摘要) 本研究提出作答反應與反應時間聯合模式（RT-IRT 模式）的三個新擴展。這些擴展是貝氏統計中資料擴增 (DA) 策略的應用。具體來說，是利用 Pólya-Gamma (PG) 分配在 logistic 模式中實作 Gibbs 抽樣器，以及利用不對稱 Laplace 分配 (ALD) 在貝氏分量迴歸 (BQR) 中實作 Gibbs 抽樣器。 本論文包含三項主要研究。第一項研究將 PG Gibbs 抽樣器應用於 logistic RT-IRT 模式、第二項研究將 BQR 引進潛在迴歸的 RT-IRT 模式、第三項研究將 BQR 加入具有交叉關係的 RT-IRT 模式。 透過模擬研究和 TIMSS 2019 數學測驗的真實資料分析，本研究得到三個主要發現。第一，PG 方法比傳統方法（包括 MLE）表現更佳，尤其是在樣本較小（250 人）和測驗較短（15 題）的情況下。另外，在模擬條件下，BQR 在潛在迴歸模式和交叉關係模式上都表現有效。然而，對於 BQR 潛在迴歸模式，在不同分量位置上，迴歸係數並沒有明顯變化效果。相比之下，BQR 交叉關係模式在不同分量位置中顯示出明顯的交叉負荷，尤其在第 40 分量附近的模式適配效果更佳。 三種模式都具有良好的收斂特性，所有參數都在 5000 次迭代的預熱期內達到穩定。整體來說，PG Gibbs 抽樣有助於整合 logistic IRT 模式，而 BQR 方法比平均迴歸模式更加靈活且有效。此外，本研究利用 Julia 開發的統計套件支援上述擴展，讓研究人員能夠分析教育測驗中的 RT-IRT 模式。 zh_TW dc.description.abstract (摘要) This study proposed three new extensions of the joint modeling for responses and response times (RT-IRT models). These extensions are applications of data augmentation (DA) strategies in the Bayesian statistics. Specifically, the study utilizes the Pólya-Gamma (PG) distribution for implementing Gibbs sampler in logistic models, and the asymmetric Laplace distribution (ALD) for implementing Gibbs sampler in Bayesian quantile regressions (BQR). Three major studies were conducted. The first study applied the PG Gibbs sampler to the logistic RT-IRT models, The second study introduced the BQR to the latent regression RT-IRT models, and the third study added the BQR to the RT-IRT models with cross-relations. Through simulation studies and real data analyses using TIMSS 2019 mathematics assessment, the research revealed three key findings. One is that the PG method demonstrated better performance than traditional approaches, including MLE, particularly with smaller samples (N=250) and shorter tests (15 items). Another is that the BQR model performed effectively under simulation conditions for both latent regression and cross-relation models. However, for the BQR-based latent regression, it showed no obvious change effects of regression coefficients in different quantile levels. In contrast, the BQR-based cross-relation model shows significant cross-loadings across quantile levels, with better model fit around the 40th quantile. All three models showed good convergence properties, with parameters stabilizing within the burn-in 5000 iterations. Overall, the PG Gibbs sampling facilitates the incorporation of logistic IRT models, while BQR approaches are more flexible and effective than mean regression models. Moreover, a statistical package developed in Julia supports these extensions, enabling researchers to analyze RT-IRT models in educational testing. en_US dc.description.tableofcontents 1 Introduction 1 1.1 Background and Motivation 1 1.2 This Current Study 4 1.3 Additional Information 7 2 Literature Review 13 2.1 Distributions of Response Time Modeling 13 2.2 Joint Modeling Framework for Item Responses and Response Times 14 2.3 Conditional Dependence Issues of Joint Modeling 18 3 Pólya-Gamma Gibbs Sampler for RT-IRT Modeling 23 3.1 Introduction 23 3.2 Methods 33 3.3 Results 36 4 Bayesian Quantile Latent Variable Regression RT-IRT Modeling 45 4.1 Introduction 45 4.2 Methods 51 4.3 Results 54 5 Bayesian Quantile Cross-Relation RT-IRT Modeling 73 5.1 Introduction 73 5.2 Methods 80 5.3 Results 82 6 General Discussion 103 6.1 Key Findings 103 6.2 Connecting the Findings 106 6.3 Recommendation 108 6.4 Limitations and Future Directions 110 Reference 113 Appendices 129 A. The Julia Package ExtendedRtIrtModeling.jl 129 B. Mplus codes for three real data analyses 134 C. JAGS codes for for three real data analyses 138 zh_TW dc.format.extent 8391381 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109152512 en_US dc.subject (關鍵詞) 試題反應模式 zh_TW dc.subject (關鍵詞) 反應時間模式 zh_TW dc.subject (關鍵詞) Gibbs抽樣 zh_TW dc.subject (關鍵詞) Pólya-Gamma分配 zh_TW dc.subject (關鍵詞) 不對稱 Laplace分配 zh_TW dc.subject (關鍵詞) item response modeling en_US dc.subject (關鍵詞) response time modeling en_US dc.subject (關鍵詞) Gibbs sampler en_US dc.subject (關鍵詞) Pólya-Gamma distribution en_US dc.subject (關鍵詞) asymmetric Laplace distribution en_US dc.title (題名) 作答反應與反應時間聯合模式的擴展與應用 zh_TW dc.title (題名) Extensions and applications of joint modeling for responses and response times en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Albert, J. H. (1992). 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